Linear increment chain and ratio: A total of ₹ 300 is divided among P, Q, and R such that Q gets ₹ 30 more than P, and R gets ₹ 60 more than Q. Determine the ratio of their shares (P : Q : R) and verify against the total.

Introduction / Context:
When sequential differences are given, define one variable and express the others relatively. The ratio emerges naturally after solving for the base amount using the total sum constraint, and then simplifying the three values to a ratio.

Given Data / Assumptions:

• Total = ₹ 300.
• Q = P + 30; R = Q + 60 = P + 90.

Concept / Approach:
Let P = p. Then Q = p + 30 and R = p + 90. Use p + (p + 30) + (p + 90) = 300 to find p. Then compute P : Q : R and simplify to lowest terms.

Step-by-Step Solution:

Verification / Alternative check:
Check differences: Q − P = 30 and R − Q = 60; sum is 60 + 90 + 150 = 300, consistent.

Why Other Options Are Wrong:
3 : 2 : 5, 2 : 5 : 3, 5 : 3 : 2, and 4 : 5 : 6 do not meet the stated difference conditions simultaneously.

Common Pitfalls:
Reversing the difference directions (e.g., subtracting rather than adding) or forgetting to apply both increments before forming the ratio.

Final Answer:
2 : 3 : 5